Non-periodic driving of coupled oscillators:a spherical swing

Nonlinearly coupled, damped oscillators at 1:1 frequency ratio, one oscillator being driven coherently for efficient excitation, are exemplified by a spherical swing with some phase-mismatch between drive and response. For certain damping range, excitation is found to succeed if it lags behind, but to produce a chaotic attractor if it leads the response. Although a period-doubhng sequence, for damping increasing, leads to the attractor, this is actually born as a hard (as regards amplitude) bifurcation at a zero growth-rate parametric line; as damping decreases, an unstable fixed point crosses an invariant plane to enter as saddle-focus a phase-space domain of physical solutions. A second hard bifurcation occurs at the zero mismatch line, the saddle-focus leaving that domain. Times on the attractor diverge when approaching either fine, leading to exactly one-dimensional and noninvertible limit maps, which are analytically determined.

Reentrant and whirling hexagons in non-Boussinesq convection

We review recent computational results for hexagon patterns in non- Boussinesq convection. For sufficiently strong dependence of the fluid parameters on the temperature we find reentrance of steady hexagons, i.e. while near onset the hexagon patterns become unstable to rolls as usually, they become again stable in the strongly nonlinear regime. If the convection apparatus is rotated about a vertical axis the transition from hexagons to rolls is replaced by a Hopf bifurcation to whirling hexagons. For weak non-Boussinesq effects they display defect chaos of the type described by the two-dimensional (2D) complex Ginzburg-andau equation. For stronger non-Boussinesq effects the Hopf bifurcation becomes subcritical and localized bursting of the whirling amplitude is found. In this regime the cou- pling of the whirling amplitude to (small) deformations of the hexagon lattice becomes important. For yet stronger non-Boussinesq effects this coupling breaks up the hexagon lattice and strongly disordered states characterized by whirling and lattice defects are obtained.

Defect chaos and bursts: Hexagonal rotating convection and the complex Ginzburg-Landau equation

We employ numerical computations of the full Navier-Stokes equations to investigate non-Boussinesq convection in a rotating system using water as the working fluid. We identify two regimes. For weak non- Boussinesq effects the Hopf bifurcation from steady to oscillating (whirling) hexagons is supercritical and typical states exhibit defect chaos that is systematically described by the cubic complex Ginzburg-Landau equation. For stronger non-Boussinesq effects the Hopf bifurcation becomes subcritical and the oscil- lations exhibit localized chaotic bursting, which is modeled by a quintic complex Ginzburg-Landau equation.

Zero-G Gauging systems. CONTRACT No 17/8/4

Various systems for measuring propellant content in spacecrafts under weightlessness conditions are reviewed. The cavity resonator method is found to be the most suitable measurement; technique. This method is analyzed in detail. A determination of errors intrinsec to the method is carried out.

Hybrid analysis of nonlinear circuits: DAE models with indices zero and one

We extend in this paper some previous results concerning the differential-algebraic index of hybrid models of electrical and electronic circuits. Specifically, we present a comprehensive index characterization which holds without passivity requirements, in contrast to previous approaches, and which applies to nonlinear circuits composed of uncoupled, one-port devices. The index conditions, which are stated in terms of the forest structure of certain digraph minors, do not depend on the specific tree chosen in the formulation of the hybrid equations. Additionally, we show how to include memristors in hybrid circuit models; in this direction, we extend the index analysis to circuits including active memristors, which have been recently used in the design of nonlinear oscillators and chaotic circuits. We also discuss the extension of these results to circuits with controlled sources, making our framework of interest in the analysis of circuits with transistors, amplifiers, and other multiterminal devices.

Bifurcation diagrams for polymer blends with diffuse interfaces in confined and adaptive geometries

Dynamics of binary mixtures such as polymer blends, and fluids near the critical point, is described by the model-H, which couples momentum transport and diffusion of the components [1]. We present an extended version of the model-H that allows to study the combined effect of phase separation in a polymer blend and surface structuring of the film itself [2]. We apply it to analyze the stability of vertically stratified base states on extended films of polymer blends and show that convective transport leads to new mechanisms of instability as compared to the simpler diffusive case described by the Cahn- Hilliard model [3, 4]. We carry out this analysis for realistic parameters of polymer blends used in experimental setups such as PS/PVME. However, geometrically more complicated states involving lateral structuring, strong deflections of the free surface, oblique diffuse interfaces, checkerboard modes, or droplets of a component above of the other are possible at critical composition solving the Cahn Hilliard equation in the static limit for rectangular domains [5, 6] or with deformable free surfaces [6]. We extend these results for off-critical compositions, since balanced overall composition in experiments are unusual. In particular, we study steady nonlinear solutions of the Cahn-Hilliard equation for bidimensional layers with fixed geometry and deformable free surface. Furthermore we distinguished the cases with and without energetic bias at the free surface. We present bifurcation diagrams for off-critical films of polymer blends with free surfaces, showing their free energy, and the L2-norms of surface deflection and the concentration field, as a function of lateral domain size and mean composition. Simultaneously, we look at spatial dependent profiles of the height and concentration. To treat the problem of films with arbitrary surface deflections our calculations are based on minimizing the free energy functional at given composition and geometric constraints using a variational approach based on the Cahn-Hilliard equation. The problem is solved numerically using the finite element method (FEM).

Direct and adjoint global stability analysis of turbulent transonic flows over a NACA0012 profile

In this work, various turbulent solutions of the two-dimensional (2D) and three-dimensional compressible Reynolds averaged Navier?Stokes equations are analyzed using global stability theory. This analysis is motivated by the onset of flow unsteadiness (Hopf bifurcation) for transonic buffet conditions where moderately high Reynolds numbers and compressible effects must be considered. The buffet phenomenon involves a complex interaction between the separated flow and a shock wave. The efficient numerical methodology presented in this paper predicts the critical parameters, namely, the angle of attack and Mach and Reynolds numbers beyond which the onset of flow unsteadiness appears. The geometry, a NACA0012 profile, and flow parameters selected reproduce situations of practical interest for aeronautical applications. The numerical computation is performed in three steps. First, a steady baseflow solution is obtained; second, the Jacobian matrix for the RANS equations based on a finite volume discretization is computed; and finally, the generalized eigenvalue problem is derived when the baseflow is linearly perturbed. The methodology is validated predicting the 2D Hopf bifurcation for a circular cylinder under laminar flow condition. This benchmark shows good agreement with the previous published computations and experimental data. In the transonic buffet case, the baseflow is computed using the Spalart?Allmaras turbulence model and represents a mean flow where the high frequency content and length scales of the order of the shear-layer thickness have been averaged. The lower frequency content is assumed to be decoupled from the high frequencies, thus allowing a stability analysis to be performed on the low frequency range. In addition, results of the corresponding adjoint problem and the sensitivity map are provided for the first time for the buffet problem. Finally, an extruded three-dimensional geometry of the NACA0012 airfoil, where all velocity components are considered, was also analyzed as a Triglobal stability case, and the outcoming results were compared to the previous 2D limited model, confirming that the buffet onset is well detected.

Energy efficiency evaluation of zero energy houses

Given the global energy and environmental situation, the European Union has been issuing directives with increasingly demanding requirements in term of the energy efficiency in buildings. The international competition of sustainable houses, Solar Decathlon Europe (SDE), is aligned with these European objectives. SDE houses are low energy solar buildings that must reach the near to zero energy houses’ goal. In the 2012 edition, in order to emphasize its significance, the Energy Efficiency Contest was added. SDE houses’ interior comfort, functioning and energy performance is monitored. The monitoring data can give an idea about the efficiency of the houses. However, a jury comprised by international experts is responsible for carrying out the houses energy efficiency evaluation. Passive strategies and houses services are analyzed. Additionally, the jury's assessment has been compared with the behavior of the houses during the monitoring period. Comparative studies make emphasis on the energy aspects, houses functioning and their interior comfort. Conclusions include thoughts related with the evaluation process, the results of the comparative studies and suggestions for the next competitions.

Pulsiones del espacio : Oteiza y la aproximación a la arquitectura como vacío activo

Este trabajo se centra en el estudio de las investigaciones de Jorge Oteiza en torno a la funcionalidad estética del espacio, en especial, en la actividad artística que desarrolló en el año 1958, un año decisivo en la vida del escultor en el que dio por finalizado su proceso de experimentación sobre la naturaleza espacial de la estatua. En este desenlace tuvo un papel fundamental la relación funcional que planteó, a la hora de retomar su trabajo después de su triunfo en la IV Bienal de São Paulo de 1957, entre la escultura y la arquitectura. La primera, entendida como organismo puramente espacial, debía de responder a las condiciones de su mundo circundante, el espacio arquitectónico. Su función: acondicionarlo estéticamente para satisfacer las necesidades espirituales del habitante. Siguiendo el canon estético que para la escultura acababa de anunciar en Brasil, la desocupación espacial (la liberación de la energía espacial de la estatua, el rompimiento de la neutralidad del espacio libre) no se trataba de embellecer superficialmente la arquitectura sino de activar su vacío interior. Oteiza, que siempre estuvo muy interesado por la arquitectura y que había colaborado con anterioridad en numerosas ocasiones con los mejores arquitectos del país, fue durante este año cuando profundizó de manera más sistemática (teórica y prácticamente) sobre la relación arte-arquitectura. De hecho, él mismo nombraba como el último trabajo de su línea de experimentación en escultura a su propuesta para el concurso del Monumento a José Batlle en Montevideo, que junto al arquitecto Roberto Puig acabaron a finales de año. En el proyecto se planteaba a escala urbana, y como ejemplo concreto, el modelo teórico de integración arquitectura + (arte=0) que había elaborado los meses anteriores, la integración vacía. En el texto explicativo que acompañaba al proyecto (un texto que desbordaba los límites de una memoria al uso) demandaba la necesidad de la toma de conciencia estética del espacio, como acto de libertad individual, y declaraba el fin del rol de espectador del hombre frente a la obra de arte, reclamando su participación activa en la misma. Para él, la noción del espacio estético no era una condición innata en el hombre, se descubría, se aprendía, evolucionaba y se olvidaba (una vez convertido en hábito). Frente a la ceguera de la sensibilidad espacial del hombre, proponía la educación de la percepción espacial, condicionar emocionalmente la reflexión espontánea ante el juego espacial de las formas en la naturaleza y el espectáculo natural de la ciudad. Aprender a leer el lenguaje emocional del espacio, a pensar visualmente. La obra de arte era así un catalizador espiritual del contorno del mundo, modificador de la vida espacial circundante que corregía hábitos visuales y condicionaba estímulos y reflejos. Desde una resonancia afectiva con la definición psicológica del término (como energía psíquica profunda que invita o incita a pasar a la acción), a diferencia del instinto, la pulsión (siendo la fuente de toda conducta espontánea) es susceptible de ser modificada por la experiencia, por la educación, por la cultura, por el deseo. Es desde esta aproximación en términos de energía desde la que se propone la noción pulsiones del espacio como fórmula (reversible) entre la energía espacial liberada en el proceso de desocupación definido por Oteiza y caracterizadora de la obra como vacío activo (en escultura, en arquitectura), y la energía psíquica profunda que invita o incita a la toma de posesión del espacio (la voluntad espacial absoluta con la que Oteiza definía su modelo de arte=0, cero como expresión formal). Si el hombre modifica su entorno al mismo tiempo que es condicionado por él, es indispensable una conciencia estética del espacio que le enseñe, de entre todas las posibilidades que este le ofrece, qué es lo que necesita (qué es lo que le falta), para tomar posesión de él, para un efectivo ser o existir en el espacio. Es desde esta caracterización como energía por lo que las pulsiones del espacio se sitúan entre el hombre y su entorno (construido) y permiten la transformación entre energía espacial y energía psíquica; entre su hábitat y sus hábitos. Por estas mismas fechas, Oteiza definía una casa como un conjunto articulado de vacíos activos, como una obra de plástica pura que no es arte sino en función del habitante. Es este habitante, educado en la toma de conciencia estética del espacio, el que participando activamente en la interpretación de los espacios previstos por el arquitecto, sintiendo y movido por las pulsiones del espacio, hará uso adecuado de la arquitectura; pasando de un arte como objeto a un arte como comportamiento, transformará su habitar en un arte, el arte de habitar. ABSTRACT This work focuses on the study of Jorge Oteiza’s investigations on the aesthetic functionality of space, especially on his artistic activity developed in 1958, a decisive year in the life of the sculptor, in which he gave end to his process of experimentation on the spatial nature of the statue. In this outcome it was fundamental the functional relationship that he propounded, at the time of returning to work after his triumph in the IV Bienal de São Paulo in 1957, between sculpture and architecture. The first, understood as a purely spatial organism, should respond to the conditions of its environment (umwelt), the architectonic space. Its function: set it up aesthetically to meet the spiritual needs of the inhabitant. Following the aesthetic canon that he had just announced in Brazil for sculpture, the spatial disoccupation (the liberation of the spatial energy of the statue, the breaking of the neutrality of the free space) the aim was not to superficially beautify architecture but to activate its inner void. Oteiza, who had always been very interested in architecture and who had previously collaborated on numerous occasions with the best architects in the country, was in this year when he deepened in a more systematic way (theoretically and practically) about the art-architecture relationship. In fact, he named as the last work of his line of experimentation in sculpture to his proposal for the competition of the Monument to José Batlle in Montevideo, which, developed together with the architect Roberto Puig, was ended at the end of the year. The project proposed on an urban scale, and as a concrete example, the theoretical model of integration architecture + (art = 0) which he had elaborated the previous months, the empty integration. In the explanatory text accompanying the project (a text that exceeded the normal extents of a competition statement) he demanded the need of the aesthetic awareness of space, as an act of individual freedom, and it declared the end of the role of man as passive spectator in front of the work of art, claiming his actively participation in it. For him, the notion of the aesthetic space was not an inborn condition in man; first it was discovered, then learned, evolved and finally forgotten (once converted into a habit). To counteract blindness of the spatial sensitivity of man, he proposed the education of spatial perception, to emotionally influence the spontaneous reflection in front of the spatial game of forms in nature and the natural spectacle of the city. Learn to read the emotional language of space, to think visually. The work of art was thus a spiritual catalyst of the world’s contour, a modifier of the surrounding spatial life that corrected visual habits and conditioned stimuli and reflexes. From an emotional resonance with the psychological definition of the term (such as deep psychic power that invites or urges action), as opposed to instinct, drive (being the source of all spontaneous behavior) is likely to be modified by experience, by education, by culture, by desire. It is from this approach in terms of energy from which the notion drives of space is proposed, as a (reversible) formula between the spatial energy released in the process of disoccupation defined by Oteiza and characterizing of the work as a charged void (in sculpture, in architecture), and the deep psychic energy that invites or encourages the taking possession of the space (the absolute spatial will with which Oteiza defined its model of Art = 0, zero as a formal expression). If man changes his environment at the same time that is conditioned by it, it is essential an aesthetic awareness of space that shows him, among all the possibilities that it offers, what he needs (what is what he lacks), in order to take possession of it, for an effective being or existing in space. It is this characterization as energy by what drives of space lie between man and his (built) environment and allow the transformation between spatial and psychological energy; between his habitat and his habits. Around this same time, Oteiza defined a House as an articulated set of charged voids, as a work of pure plastic that is not art but according to the inhabitant. It is this inhabitant, educated in aesthetic awareness of space, who actively participating in the interpretation of the spaces provided by the architect, feeling and moved by the drives of the space, will make proper use of the architecture; from an art as object to an art as behavior, he will transform his inhabitation into an art, the art of inhabitation.